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1 results

  • Mixing properties for STIT tessellations

  • Part of
  • R. Lachièze-Rey
  • Journal:
    Advances in Applied Probability / Volume 43 / Issue 1 / March 2011
    Published online by Cambridge University Press:
    01 July 2016, pp. 40-48
    Print publication:
    March 2011
    • Article
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  • The so-called STIT tessellations form a class of homogeneous (spatially stationary) tessellations in Rd which are stable under the nesting/iteration operation. In this paper we establish the mixing property for these tessellations and give the decay rate of P(A ∩ M = ∅, ThB ∩ M = ∅) / P(A ∩ Y = ∅)P(B ∩ Y = ∅) − 1, where A and B are both compact connected sets, h is a vector of Rd, Th is the corresponding translation operator, and M is a STIT tessellation.